filtered outliers by utilizing bins and distance-based adaptive thresholds. Zhu et al. 2011 projected MLS data to three
orthogonal planes and divided them into bins, with a threshold for the bins that contained too few points. Vaaja et al. 2013
detected outlier points by searching if there was less than ten points within a 0.50 meters radius. TerraScan also examines
spherical area with given radius when removing unwanted air points utilizing median elevations and standard deviations
TerraScan. To conclude, the noise filtering in these works is based on the assumption that full information is available in the
3D neighborhood of the point in focus. Therefore, the GNSS- scene approach is unsuitable for our needs, as the filtering must
take place before the ICP-based registration.
In this paper, we present an inherently local outlier filtering method that is optimized for MLS data, and takes place before
the ICP-based registration. Then we show how to correct the relative orientations between the laser scanning profiles
obtained from the theoretical solution of Lehtola et al., 2015.
The paper is organized as follows. The 1D theoretical solution for intrinsic localization is briefly summarized in Section 2.
Then, the data processing is done in two steps. First, mobile laser scanner data is filtered, for which we introduce a novel
concept of local range support in Section 3.1. Second, a semi- global point cloud matching using 3DTK 6D SLAM is done to
adjust the trajectory to its environment, leading to a 3D solution. This is presented in Section 3.2. Results are shown in
Section 4, after which follows the Conclusion.
2. INTRINSIC LOCALIZATION FOR A ONE- DIMENSIONAL TRAJECTORY
The localization of the laser data requires a successful reconstruction of the sensor trajectory. The trajectory jt is
time-dependent with six degrees of freedom, namely, three from location and three from orientation. We write out
j t = [
θ
t
, ψ
t
, φ
t,x t ,y t ,z t ]
1 where
θ is the pitch, ψ is the roll, and φ is the yaw angle. Time is denoted by t. Without any reference coordinate system, the
successful reconstruction of the trajectory requires that these degrees of freedom are eliminated. Previously, this was done by
Lehtola et al. 2015 for a holonomic system in one dimension 1D. We briefly outline this solution here.
In order to capture a 3D environment with a 2D laser scanner, the scanner must be rotated about at least one axis. The 2D
scanner is mechanically attached to the platform, so that it can only rotate about one axis of rotation, namely
θ. Therefore rotational degrees of freedom are reduced by two, i.e.
φ and ψ are constant. By assuming that the platform does not slip against
the floor x, y, and z all become direct functions of θ.
The scanner sits on the hypotenuse at a distance of R − R
1
from VILMA’s central axis, where R
= 0.25m is the radius of the metal disc and R
1
= 0.13m, see Fig. 1 a. Assuming that the floor is flat, simple trigonometry is employed to write
=
arccos
, 2
where d = d
m
+ R − R
1
, and d
m
is the minimum measured distance to the
floor over one full 2D circle observation. Considering the minimum distance to the
floor, the position of the scanner on disk radius varies between two values, depending
on whether the scanner is upside down, Eq. 2, or upside up, in which case
θ = π – arccos R d, with d = R
+ cos 27.5
◦
d
m
− R
2
, and R
2
= 42cm. Here, the 27.5 degrees is half of the dead angle of the scanner.
The pitch angle θt is the path parameter that describes the
scanner trajectory, and obtaining it from the scanner data solves localization in 1D. Initially, the zenith is pointing upwards,
θt =0 = 0. Then,
θ is incremented by 2π for each cycle that the platform rolls. Each time the 2D scanner is perpendicular
towards the floor PTF, θt = π + 2πn, n = 0, 1, 2, ..., the
scanning distance reduces to the minimum R
1
. We call this a PTF-observation, and keep track of these occurrences in the
laser data obtaining a time series. The PTF observation is robust to error, since data points from a large
field of view can be used to interpolate the
floor point precisely below the sensor. Also, stochastic errors in PTF observations do not cumulate with time
as long as the no-slip condition with the floor applies.
Once θt is obtained, a coordinate transformation for the 2D
sensor data X, Z is obtained considering the trajectory of a contracted cycloid,
= =
θ
+
− +
sin
θ
z = +
−
+ Z cos
θ 3
where x,y,z are the coordinates of the resulting 3D point cloud. Note that the platform propagates in the positive y-
direction.
3. METHODS
